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Dont seem to find any discussion of this question in the master thread.

If two lines have slopes m and n, respectively, are they perpendicular?

(a) m*n = -1(b) m = -n

My question is why the OA is not D? Is it correct that based on the second option, we can conclude that the answer is NO?

Am I missing something? Pls help.

For one line to be perpendicular to another, the relationship between their slopes has to be negative reciprocal, so if the slope of one line is \(m\) then the line prependicular to it will have the slope \(-\frac{1}{m}\). In other words, the [highlight]two lines are perpendicular if and only the product of their slopes is -1[/highlight].

If two lines have slopes m and n, respectively, are they perpendicular?

(1) m*n = -1 --> directly gives an answer YES to the question.

(2) m = -n --> now, if for example m=3=-(-3)=-n then the lines are not perpendicular but if m=1=-(-1)=-n (or m=-1=-1=-n) then as mn would be equal to -1 the lines would be perpendicular. Not sufficient.

Answer: A.

Matt1177 you should have spotted that there was something wrong with your solution as on the GMAT, [highlight]two data sufficiency statements always provide TRUE information and these statements never contradict each other[/highlight].

So we can not have answer YES from statement (1) and answer NO from statement (2), as in this case statements would contradict each other.

Hope it helps.

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